Jointly modeling responses and omitted items by a competing risk model: A survival analysis approach.

Item response theory models are commonly adopted in educational assessment and psychological measurement. Such models need to be modified to accommodate practical situations when statistical sampling assumptions are violated. Omission is a common phenomenon in educational testing. In modern computer-based testing, we have not only examinees' responses but also their response times. This paper utilizes response time and develops a joint model of responses and response times. The new approach is analogous to those developed in survival analysis for dealing with right-censored data. In particular, a key ingredient is the introduction of the omission time (OT), which corresponds to the censoring time in survival analysis. By competing risk formulation, the proposed method provides an alternative narrative to how an item becomes answered versus omitted, depending on the competing relationship of response time and OT, so that the likelihood function can be constructed properly. The maximum likelihood estimator can be computed via the expectation-maximization algorithm. Simulation studies were conducted to evaluate the performance of the proposed method and its robustness against various mis-specifications. The method was applied to a dataset from the PISA 2015 Science Test.